Portfolio analysis with DEA: Prior to choosing a model

This paper aims at providing answers to the questions raised in Cook et al. (2014) in the context of portfolio analysis with Data Envelopment Analysis (DEA). This reflection leads to define the financial production process as the generation of a distribution of returns by an initial investment. The main contribution of the paper is therefore to consider risks of various orders – mean return, variance of returns, and moments of higher order – as output variables and propose a set of axioms accordingly to supplement the definition of ‘financial’ technology set. In particular, this revisited set of axioms offers the advantage of allowing a generalization to multi-moment frameworks, and the resulting portfolio possibility set allows taking into account preferences for increases in risk that have remained ignored in applied studies with DEA although discussed in economic theory. We provide illustrations to show the effects of this contribution on the measures of technical efficiency and ranking of portfolios on a sample set of US common stocks; it shows how the proposed adjustments result in providing rankings that are more consistent with standard risk-return ratios in finance.